Changeset 4774 for branches/2014/dev_r4650_UKMO12_CFL_diags_take2/DOC/TexFiles/Chapters/Chap_DIA.tex

Timestamp:

2014-09-18T14:36:51+02:00 (10 years ago)

Author:

timgraham

Message:

Updated documentation to describe new diagnostics.

File:

• branches/2014/dev_r4650_UKMO12_CFL_diags_take2/DOC/TexFiles/Chapters/Chap_DIA.tex (modified) (1 diff)

branches/2014/dev_r4650_UKMO12_CFL_diags_take2/DOC/TexFiles/Chapters/Chap_DIA.tex

@@ -1386 +1386 @@
 \\
 
+\section{Courant numbers}
+Courant numbers provide a theoretical indication of the model's numerical stability. The advective Courant numbers can be calculated according to
+\begin{equation}
+\label{eq:CFL}
+C_u = |u|\frac{\rdt}{e_{1u}}, \quad C_v = |v|\frac{\rdt}{e_{2v}}, \quad C_w = |w|\frac{\rdt}{e_{3w}}
+\end{equation}
+in the zonal, meridional and vertical directions respectively. The vertical component is included although it is not strictly valid as the vertical velocity is calculated from the continuity equation rather than as a prognostic variable. Physically this represents the rate at which information is propogated across a grid cell. Values greater than 1 indicate that information is propagated across more than one grid cell in a single time step.
+
+The variables can be activated by setting the \np{nn\_diacfl} namelist parameter to 1 in the \ngn{namctl} namelist. The diagnostics will be written out to an ascii file named cfl\_diagnostics.ascii. In this file the maximum value of $C_u$, $C_v$, and $C_w$ are printed at each timestep along with the coordinates of where the maximum value occurs. At the end of the model run the maximum value of $C_u$, $C_v$, and $C_w$ for the whole model run is printed along with the coordinates of each. The maximum values from the run are also copied to the ocean.output file.